Chansangiam, Pattrawut

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Chansangiam, Pattrawut
Alternative Name
Chansangiam, P.
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pattrawut.ch@kmitl.ac.th

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    Solving the Sylvester-Transpose Matrix Equation under the Semi-Tensor Product
    (2022-06-01)
    Jaiprasert, Janthip
    ;
    Chansangiam, Pattrawut
    This paper investigates the Sylvester-transpose matrix equation A ⋉ X + X<sup>T</sup> ⋉ B = C, where all mentioned matrices are over an arbitrary field. Here, ⋉ is the semi-tensor product, which is a generalization of the usual matrix product defined for matrices of arbitrary dimensions. For matrices of compatible dimensions, we investigate criteria for the equation to have a solution, a unique solution, or infinitely many solutions. These conditions rely on ranks and linear dependence. Moreover, we find suitable matrix partitions so that the matrix equation can be transformed into a linear system involving the usual matrix product. Our work includes the studies of the equation A ⋉ X = C, the equation X ⋉ B = C, and the classical Sylvester-transpose matrix equation.
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    Exact and least-squares solutions of a generalized Sylvester-transpose matrix equation over generalized quaternions
    (2024-01-01)
    Jaiprasert, Janthip
    ;
    Chansangiam, Pattrawut
    We have considered a generalized Sylvester-transpose matrix equation AXB + CXTD = E, where A, B,C, D, and E are given rectangular matrices over a generalized quaternion skew-field, and X is an unknown matrix. We have applied certain vectorizations and real representations to transform the matrix equation into a matrix equation over the real numbers. Thus, we have investigated a solvability condition, general exact/least-squares solutions, minimal-norm solutions, and the exact/least-squares solution closest to a given matrix. The main equation included the equation AXB = E and the Sylvester-transpose equation. Our results also covered such matrix equations over the quaternions, and quaternionic linear systems.